(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
b(f(b(x, z)), y) → f(f(f(b(z, b(y, z)))))
c(f(f(c(x, a, z))), a, y) → b(y, f(b(a, z)))
b(b(c(b(a, a), a, z), f(a)), y) → z
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
B(f(b(x, z)), y) → B(z, b(y, z))
B(f(b(x, z)), y) → B(y, z)
C(f(f(c(x, a, z))), a, y) → B(y, f(b(a, z)))
C(f(f(c(x, a, z))), a, y) → B(a, z)
The TRS R consists of the following rules:
b(f(b(x, z)), y) → f(f(f(b(z, b(y, z)))))
c(f(f(c(x, a, z))), a, y) → b(y, f(b(a, z)))
b(b(c(b(a, a), a, z), f(a)), y) → z
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
B(f(b(x, z)), y) → B(y, z)
B(f(b(x, z)), y) → B(z, b(y, z))
The TRS R consists of the following rules:
b(f(b(x, z)), y) → f(f(f(b(z, b(y, z)))))
c(f(f(c(x, a, z))), a, y) → b(y, f(b(a, z)))
b(b(c(b(a, a), a, z), f(a)), y) → z
Q is empty.
We have to consider all minimal (P,Q,R)-chains.